quasirandom.py

import torch
from typing import Optional


class SobolEngine:
    r"""
    The :class:`torch.quasirandom.SobolEngine` is an engine for generating
    (scrambled) Sobol sequences. Sobol sequences are an example of low
    discrepancy quasi-random sequences.

    This implementation of an engine for Sobol sequences is capable of
    sampling sequences up to a maximum dimension of 21201. It uses direction
    numbers from https://web.maths.unsw.edu.au/~fkuo/sobol/ obtained using the
    search criterion D(6) up to the dimension 21201. This is the recommended
    choice by the authors.

    References:
      - Art B. Owen. Scrambling Sobol and Niederreiter-Xing points.
        Journal of Complexity, 14(4):466-489, December 1998.

      - I. M. Sobol. The distribution of points in a cube and the accurate
        evaluation of integrals.
        Zh. Vychisl. Mat. i Mat. Phys., 7:784-802, 1967.

    Args:
        dimension (Int): The dimensionality of the sequence to be drawn
        scramble (bool, optional): Setting this to ``True`` will produce
                                   scrambled Sobol sequences. Scrambling is
                                   capable of producing better Sobol
                                   sequences. Default: ``False``.
        seed (Int, optional): This is the seed for the scrambling. The seed
                              of the random number generator is set to this,
                              if specified. Otherwise, it uses a random seed.
                              Default: ``None``

    Examples::

        >>> # xdoctest: +SKIP("unseeded random state")
        >>> soboleng = torch.quasirandom.SobolEngine(dimension=5)
        >>> soboleng.draw(3)
        tensor([[0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                [0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
                [0.7500, 0.2500, 0.2500, 0.2500, 0.7500]])
    """
    MAXBIT = 30
    MAXDIM = 21201

    def __init__(self, dimension, scramble=False, seed=None):
        if dimension > self.MAXDIM or dimension < 1:
            raise ValueError("Supported range of dimensionality "
                             f"for SobolEngine is [1, {self.MAXDIM}]")

        self.seed = seed
        self.scramble = scramble
        self.dimension = dimension

        cpu = torch.device("cpu")

        self.sobolstate = torch.zeros(dimension, self.MAXBIT, device=cpu, dtype=torch.long)
        torch._sobol_engine_initialize_state_(self.sobolstate, self.dimension)

        if not self.scramble:
            self.shift = torch.zeros(self.dimension, device=cpu, dtype=torch.long)
        else:
            self._scramble()

        self.quasi = self.shift.clone(memory_format=torch.contiguous_format)
        self._first_point = (self.quasi / 2 ** self.MAXBIT).reshape(1, -1)
        self.num_generated = 0

    def draw(self, n: int = 1, out: Optional[torch.Tensor] = None,
             dtype: torch.dtype = torch.float32) -> torch.Tensor:
        r"""
        Function to draw a sequence of :attr:`n` points from a Sobol sequence.
        Note that the samples are dependent on the previous samples. The size
        of the result is :math:`(n, dimension)`.

        Args:
            n (Int, optional): The length of sequence of points to draw.
                               Default: 1
            out (Tensor, optional): The output tensor
            dtype (:class:`torch.dtype`, optional): the desired data type of the
                                                    returned tensor.
                                                    Default: ``torch.float32``
        """
        if self.num_generated == 0:
            if n == 1:
                result = self._first_point.to(dtype)
            else:
                result, self.quasi = torch._sobol_engine_draw(
                    self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated, dtype=dtype,
                )
                result = torch.cat((self._first_point, result), dim=-2)
        else:
            result, self.quasi = torch._sobol_engine_draw(
                self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1, dtype=dtype,
            )

        self.num_generated += n

        if out is not None:
            out.resize_as_(result).copy_(result)
            return out

        return result

    def draw_base2(self, m: int, out: Optional[torch.Tensor] = None,
                   dtype: torch.dtype = torch.float32) -> torch.Tensor:
        r"""
        Function to draw a sequence of :attr:`2**m` points from a Sobol sequence.
        Note that the samples are dependent on the previous samples. The size
        of the result is :math:`(2**m, dimension)`.

        Args:
            m (Int): The (base2) exponent of the number of points to draw.
            out (Tensor, optional): The output tensor
            dtype (:class:`torch.dtype`, optional): the desired data type of the
                                                    returned tensor.
                                                    Default: ``torch.float32``
        """
        n = 2 ** m
        total_n = self.num_generated + n
        if not (total_n & (total_n - 1) == 0):
            raise ValueError("The balance properties of Sobol' points require "
                             "n to be a power of 2. {0} points have been "
                             "previously generated, then: n={0}+2**{1}={2}. "
                             "If you still want to do this, please use "
                             "'SobolEngine.draw()' instead."
                             .format(self.num_generated, m, total_n))
        return self.draw(n=n, out=out, dtype=dtype)

    def reset(self):
        r"""
        Function to reset the ``SobolEngine`` to base state.
        """
        self.quasi.copy_(self.shift)
        self.num_generated = 0
        return self

    def fast_forward(self, n):
        r"""
        Function to fast-forward the state of the ``SobolEngine`` by
        :attr:`n` steps. This is equivalent to drawing :attr:`n` samples
        without using the samples.

        Args:
            n (Int): The number of steps to fast-forward by.
        """
        if self.num_generated == 0:
            torch._sobol_engine_ff_(self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated)
        else:
            torch._sobol_engine_ff_(self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1)
        self.num_generated += n
        return self

    def _scramble(self):
        g: Optional[torch.Generator] = None
        if self.seed is not None:
            g = torch.Generator()
            g.manual_seed(self.seed)

        cpu = torch.device("cpu")

        # Generate shift vector
        shift_ints = torch.randint(2, (self.dimension, self.MAXBIT), device=cpu, generator=g)
        self.shift = torch.mv(shift_ints, torch.pow(2, torch.arange(0, self.MAXBIT, device=cpu)))

        # Generate lower triangular matrices (stacked across dimensions)
        ltm_dims = (self.dimension, self.MAXBIT, self.MAXBIT)
        ltm = torch.randint(2, ltm_dims, device=cpu, generator=g).tril()

        torch._sobol_engine_scramble_(self.sobolstate, ltm, self.dimension)

    def __repr__(self):
        fmt_string = [f'dimension={self.dimension}']
        if self.scramble:
            fmt_string += ['scramble=True']
        if self.seed is not None:
            fmt_string += [f'seed={self.seed}']
        return self.__class__.__name__ + '(' + ', '.join(fmt_string) + ')'